Question

A well of diameter 2 m is dug 14 m deep. The earth taken out of it is spread evenly all around it to a width of 5 m to form an embankment. Find the height of the embankment

• A. $0.2$
• B. $0.3$
• C. $0.4$
• D. $0.5$

Answer 1

Answer: (C)

$0.4$

Let h be the required height of the embankment. The shape of the embankment will be like the shape of a cylinder of internal radius 1 m and external radius $(5+1)m=6m$ [figure ].
The volume of the embankment will be equal to the volume of the earth dug out from the well. Now, the volume of the earth $=$ volume of the cylindrical well
$=\pi \times 1^2\times 14c{m}^3=14\pi m^3$
Also, the volume of the embankment
$=\pi (6^2-1^2)hc{m}^3=35\pi h{m}^3$
Hence, we have
$35\pi h=14\pi$
$\Rightarrow h=\frac{14}{35}=\frac{2}{5}=0.4$
Hence,the required height of the embankment $=0.4m$.